A Geometrical Approach to Iterative Isotone Regression - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Applied Mathematics and Computation Year : 2014

A Geometrical Approach to Iterative Isotone Regression

Abstract

In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic regression and the estimation of additive models. A geometrical interpretation enables us to link this iterative method with Von Neumann's algorithm. Moreover, making a connection with the general property of isotonicity of projection onto convex cones, we derive another equivalent algorithm and go further in the analysis. As iterating the algorithm leads to overfitting, several practical stopping criteria are also presented and discussed.

Dates and versions

hal-00756715 , version 1 (23-11-2012)

Identifiers

Cite

Arnaud Guyader, Nicolas Jégou, Alexander B. Németh, Sándor Z. Németh. A Geometrical Approach to Iterative Isotone Regression. Applied Mathematics and Computation, 2014, 227, pp.359-369. ⟨10.1016/j.amc.2013.11.048⟩. ⟨hal-00756715⟩
189 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More